My Comments:
There are differences between the Tamil influence, "Indian" influence, Hindu influence, and Indian Buddhist influences in this region. And by region it must include Thailand, Cambodia, Vietnam, the Indonesian archipelago with a spillover onto the Malay Peninsula.
In Indonesia the Tarumanagara, Mataram, Majapahit, Srivijaya were Indian influenced dynasties which have long lasting influence and presence in Indonesia until today. Culturally the Indonesians are still Indian and Hindu influenced. Presidents Jokowi and Prabowo Subianto often end their speeches with Om Shanti Shanti Shanti Om (Peace, Peace, Peace).
Since the Malay Peninsula is less than 24 miles from Sumatra (at Tanjong Tuan) and only 1.7 miles at the Phillips Channel in Singapore the Indonesian influence certainly spilled over onto the Peninsula. Srivijaya was a Buddhist dynasty out of Sumatera which also ruled over the Peninsula for about 400 years (7th - 11th centuries). All part of the larger Indonesian archipelago.
However the Tamil Chola dynasty had the longest lasting influence over the entire region especially in the Indonesian archipelago. The Tamil Chola Dynasty was also the longest lasting empire in human history - they lasted about 1,600 years. (The Romans are second at around 1,300 years).
Hence the overwhelming presence of Tamil and Indian vocabulary in the Malay language. Bumiputra comes from 'bhoomi' and 'putra' in Tamil. The Cholas spoke not only Tamil but were well versed in Hindu Sanskrit terminologies as well.
Hinduism significantly influenced the courts of the Malay rulers through the adoption of concepts like dewa-raja or divine kingship where the ruler held divine powers. The system of feudalism in the Malay courts was developed from the Hindu Indian idea of dewa-raja. Hindu epics were incorporated into literature and law. Titles like menteri, perdana menteri, tan sri, laksamana, bendahara are all derived from Tamil and Indian languages. This was a long and gradual process over 1,600 years assisted by the obvious perception of Indian culture as advanced.
And of course today the repository of Indian culture in the Nusantara is preserved in Indonesian dance including in Java.
